Details

sample447.0ms

Algorithm

intervals

Results

364.0ms	55×	body	2560	valid
42.0ms	86×	body	1280	valid
19.0ms	63×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	10×	body	80	valid

simplify420.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	9
1	19	9

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5196	1147

prune103.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
15.6b	(+ (* x (* x 9/40)) (+ (* (pow x 4) -27/2800) -1/2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* (pow x 4) -27/2800)
4.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
8.0ms	(+ (* x (* x 9/40)) (+ (* (pow x 4) -27/2800) -1/2))

series14.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (pow x 4) -27/2800)
3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
5.0ms	(+ (* x (* x 9/40)) (+ (* (pow x 4) -27/2800) -1/2))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4967	650
1	4967	650

prune104.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	5	91

Merged error: 0.0b

Counts

91 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

2.2b	(- x (tan x))
2.2b	(- x (sin x))
2.2b	(- x (sin x))
2.2b	(- x (sin x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

3.0ms	(- x (tan x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))

series25.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- x (tan x))
5.0ms	(- x (sin x))
4.0ms	(- x (sin x))
6.0ms	(- x (sin x))

simplify29.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4960	510
1	4960	510

prune77.0ms

Filtered

49 candidates to 68 candidates (-38.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	67	6	73

Merged error: 0.0b

Counts

73 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

2.2b	(- x (tan x))
2.2b	(- x (tan x))
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

3.0ms	(- x (tan x))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series35.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- x (tan x))
10.0ms	(- x (tan x))
12.0ms	(- x (tan x))
5.0ms	(- x (sin x))

simplify30.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4960	522
1	4960	522

prune64.0ms

Filtered

51 candidates to 68 candidates (-33.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	68	6	74

Merged error: 0.0b

Counts

74 → 6

regimes100.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch33.0ms

Steps

Iters	Range		Point
7	0.003810670139712195	0.06592465963988953	0.02894577317395436
8	-0.6973264211480649	-0.00018277710226217338	-0.02403313005852227

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	31
1	30	31

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.2s	1631×	body	2560	valid
1.7s	2785×	body	1280	valid
489.0ms	1806×	body	640	valid
180.0ms	965×	body	320	valid
57.0ms	459×	body	160	valid
27.0ms	354×	body	80	valid

Details

sample447.0ms

simplify420.0ms

prune5.0ms

localize10.0ms

rewrite30.0ms

series37.0ms

simplify47.0ms

prune103.0ms

localize9.0ms

rewrite21.0ms

series14.0ms

simplify54.0ms

prune104.0ms

localize16.0ms

rewrite14.0ms

series25.0ms

simplify29.0ms

prune77.0ms

localize12.0ms

rewrite14.0ms

series35.0ms

simplify30.0ms

prune64.0ms

regimes100.0ms

bsearch33.0ms

simplify1.0ms

end0.0ms

sample6.8s

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